Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1998 conjugacy classes of subgroups.
The subgroup lattice has 400 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86257 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#3162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83335 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #81959 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #81958 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #79181 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #79165 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #78499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#4707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #60676 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C3×#533 | C22 | 1 | 2 | yes | — |
| 12 | C2×#904 | C22 | 1 | 4 | yes | — |
| 13 | C22×ΓL(1,𝔽25) | C22 | 1 | 2 | yes | — |
| 14 | #5728 | C22 | 1 | 4 | yes | — |
| 15 | #5725 | C22 | 1 | 4 | yes | — |
| 16 | #5691 | C22 | 1 | 8 | yes | — |
| 17 | #5627 | — | 2 | 4 | no | — |
| 18 | #5624 | — | 2 | 4 | no | — |
| 19 | #5580 | — | 2 | 4 | no | — |
| 20 | C4×#239 | — | 2 | 4 | no | — |
| 21 | #5524 | C22 | 1 | 4 | yes | — |
| 22 | #5522 | C22 | 1 | 4 | yes | — |
| 23 | #5477 | C22 | 1 | 2 | yes | — |
| 24 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#501 | C22 | 1 | 8 | yes | complemented |
| 26 | C3×#427 | C22 | 1 | 4 | yes | — |
| 27 | C2×C3×#97 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C8×Dic3 | C22 | 1 | 2 | yes | — |
| 29 | #5089 | C22 | 1 | 8 | yes | complemented |
| 30 | #5069 | C22 | 1 | 4 | yes | complemented |
| 31 | #5067 | C22 | 1 | 4 | yes | complemented |
| 32 | #5002 | C22 | 1 | 8 | yes | — |
| 33 | C2×#803 | C22 | 1 | 1 | yes | characteristic |
| 34 | #4886 | C22 | 1 | 16 | yes | — |
| 35 | #4873 | C22 | 1 | 8 | yes | complemented |
| 36 | #4872 | C22 | 1 | 8 | yes | complemented |
| 37 | #4867 | C22 | 1 | 8 | yes | — |
| 38 | #4865 | C22 | 1 | 8 | yes | — |
| 39 | #4852 | C22 | 1 | 16 | yes | complemented |
| 40 | #4715 | C22 | 1 | 4 | yes | complemented |
| 41 | #4712 | C22 | 1 | 4 | yes | complemented |
| 42 | #4707 | C22 | 1 | 8 | yes | — |
| 43 | #3444 | — | 3 | 2 | no | — |
| 44 | #3172 | — | 3 | 8 | no | — |
| 45 | #3171 | — | 3 | 8 | no | — |
| 46 | #3162 | D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | #3150 | — | 3 | 1 | no | — |
| 48 | #3135 | — | 3 | 2 | no | — |
| 49 | #3054 | — | 3 | 4 | no | — |
| 50 | C4×#135 | — | 3 | 4 | no | — |
| 51 | C2×C4×M16 | — | 3 | 1 | no | — |
| 52 | C2×#239 | — | 2 | 4 | no | — |
| 53 | C2×#235 | C23 | 1 | 4 | yes | — |
| 54 | C22×C4×D3 | D4 | 1 | 2 | yes | — |
| 55 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 57 | C3×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 58 | C3×#125 | C23 | 1 | 4 | yes | — |
| 59 | C3×C22⋊Q8 | — | 2 | 4 | no | — |
| 60 | C3×C4×Q8 | — | 2 | 4 | no | — |
| 61 | C3×#117 | C23 | 1 | 4 | yes | — |
| 62 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 63 | #947 | — | 2 | 4 | no | — |
| 64 | #946 | — | 2 | 4 | no | — |
| 65 | Q8×Dic3 | — | 2 | 4 | no | — |
| 66 | #930 | — | 2 | 4 | no | — |
| 67 | C2×C4×Dic3 | D4 | 1 | 2 | yes | — |
| 68 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 70 | C2×Dic12 | C23 | 1 | 4 | yes | — |
| 71 | #904 | — | 2 | 16 | no | — |
| 72 | C2×D24 | C23 | 1 | 4 | yes | — |
| 73 | C2×#204 | C23 | 1 | 8 | yes | — |
| 74 | C2×ΓL(1,𝔽25) | — | 2 | 8 | no | — |
| 75 | C2×ΓL(1,𝔽25) | C23 | 1 | 8 | yes | — |
| 76 | #898 | — | 2 | 8 | no | — |
| 77 | #897 | C23 | 1 | 8 | yes | — |
| 78 | #895 | — | 2 | 4 | no | — |
| 79 | #895 | C23 | 1 | 8 | yes | — |
| 80 | #894 | — | 2 | 8 | no | — |
| 81 | #893 | — | 2 | 8 | no | — |
| 82 | #893 | — | 2 | 4 | no | — |
| 83 | #893 | C23 | 1 | 8 | yes | — |
| 84 | #892 | — | 2 | 4 | no | — |
| 85 | #892 | — | 2 | 8 | no | — |
| 86 | #890 | — | 2 | 4 | no | — |
| 87 | #887 | C23 | 1 | 8 | yes | — |
| 88 | #886 | — | 2 | 4 | no | — |
| 89 | #882 | — | 2 | 4 | no | — |
| 90 | #67⋊C4 | — | 2 | 8 | no | — |
| 91 | #875 | C23 | 1 | 4 | yes | — |
| 92 | #874 | C23 | 1 | 2 | yes | — |
| 93 | C4×D12 | — | 2 | 8 | no | — |
| 94 | C4×D12 | — | 2 | 4 | no | — |
| 95 | #872 | — | 2 | 4 | no | — |
| 96 | C42×D3 | — | 2 | 4 | no | — |
| 97 | C42×D3 | D4 | 1 | 2 | yes | — |
| 98 | C42×D3 | D4 | 1 | 2 | yes | — |
| 99 | C42×D3 | C23 | 1 | 4 | yes | — |
| 100 | #869 | C23 | 1 | 2 | yes | — |
| 101 | C3×#107 | C23 | 1 | 8 | yes | — |
| 102 | C3×#106 | C23 | 1 | 8 | yes | — |
| 103 | C3×#97 | C23 | 1 | 4 | yes | — |
| 104 | C8×Dic3 | C23 | 1 | 8 | yes | — |
| 105 | #810 | C23 | 1 | 16 | yes | — |
| 106 | #809 | C23 | 1 | 16 | yes | — |
| 107 | #803 | C23 | 1 | 4 | yes | — |
| 108 | C2×#135 | — | 3 | 4 | no | — |
| 109 | C22×M16 | — | 3 | 2 | no | — |
| 110 | #533 | — | 3 | 4 | no | — |
| 111 | #533 | C2×D3 | 1 | 2 | yes | — |
| 112 | #532 | — | 3 | 4 | no | — |
| 113 | #532 | — | 3 | 2 | no | — |
| 114 | #529 | — | 3 | 8 | no | — |
| 115 | #529 | — | 6 | 4 | no | — |
| 116 | #529 | — | 6 | 4 | no | — |
| 117 | #525 | — | 3 | 4 | no | — |
| 118 | #525 | — | 6 | 4 | no | — |
| 119 | C4×#41 | — | 3 | 4 | no | — |
| 120 | C4×#41 | — | 6 | 4 | no | — |
| 121 | C22×C42 | — | 3 | 1 | no | — |
| 122 | #501 | C2×D3 | 1 | 8 | yes | complemented |
| 123 | #497 | — | 3 | 4 | no | — |
| 124 | #496 | — | 3 | 4 | no | — |
| 125 | #491 | — | 3 | 4 | no | — |
| 126 | #490 | — | 3 | 4 | no | — |
| 127 | #489 | — | 3 | 8 | no | — |
| 128 | #470 | — | 3 | 8 | no | — |
| 129 | #469 | — | 3 | 8 | no | — |
| 130 | #468 | — | 3 | 16 | no | — |
| 131 | C4×Q16 | — | 3 | 8 | no | — |
| 132 | C4×SD16 | — | 3 | 16 | no | — |
| 133 | C4×D8 | — | 3 | 8 | no | — |
| 134 | #427 | C2×D3 | 1 | 4 | yes | — |
| 135 | #416 | — | 3 | 8 | no | — |
| 136 | C4×M16 | — | 3 | 8 | no | — |
| 137 | C2×#97 | — | 3 | 1 | no | — |
| 138 | C2×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C8 | — | 3 | 2 | no | — |
| 140 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 142 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 143 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 144 | C2×#67 | — | 2 | 4 | no | — |
| 145 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 146 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | #239 | — | 4 | 16 | no | — |
| 148 | #235 | — | 2 | 16 | no | — |
| 149 | C2×D12 | — | 2 | 8 | no | — |
| 150 | C2×D12 | — | 2 | 4 | no | — |
| 151 | C2×D12 | C24 | 1 | 4 | yes | — |
| 152 | C2×C4×D3 | — | 2 | 4 | no | — |
| 153 | C2×C4×D3 | — | 2 | 4 | no | — |
| 154 | C2×C4×D3 | — | 2 | 8 | no | — |
| 155 | C2×C4×D3 | — | 4 | 4 | no | — |
| 156 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 158 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 159 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 160 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 161 | C2×C3×C8 | #41 | 1 | 8 | yes | complemented |
| 162 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 163 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 164 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 165 | C3×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 166 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 167 | C3×C42 | — | 2 | 4 | no | — |
| 168 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 169 | C3×C42 | C24 | 1 | 2 | yes | — |
| 170 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 171 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 172 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 173 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 174 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 175 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 176 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 177 | C4×Dic3 | — | 2 | 8 | no | — |
| 178 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C4×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 181 | C4×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 182 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 183 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 184 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 185 | Dic12 | — | 2 | 8 | no | — |
| 186 | D24 | — | 2 | 8 | no | — |
| 187 | #204 | — | 2 | 16 | no | — |
| 188 | ΓL(1,𝔽25) | — | 2 | 16 | no | — |
| 189 | C2×#41 | — | 3 | 4 | no | — |
| 190 | C2×#41 | — | 6 | 4 | no | — |
| 191 | C23×C4 | — | 3 | 1 | no | — |
| 192 | C23×C4 | — | 3 | 2 | no | — |
| 193 | #135 | — | 6 | 16 | no | — |
| 194 | C2×Q16 | — | 3 | 4 | no | — |
| 195 | C2×SD16 | — | 3 | 8 | no | — |
| 196 | C2×D8 | — | 3 | 4 | no | — |
| 197 | C2×M16 | — | 3 | 8 | no | — |
| 198 | C2×M16 | — | 6 | 8 | no | — |
| 199 | C22×C8 | — | 3 | 2 | no | — |
| 200 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 201 | C4⋊Q8 | — | 3 | 2 | no | — |
| 202 | C4⋊Q8 | C22×D3 | 1 | 4 | yes | — |
| 203 | #127 | — | 3 | 2 | no | — |
| 204 | #126 | — | 6 | 8 | no | — |
| 205 | #125 | — | 6 | 4 | no | — |
| 206 | #125 | C22×D3 | 1 | 4 | yes | — |
| 207 | #124 | — | 3 | 4 | no | — |
| 208 | #124 | — | 6 | 4 | no | — |
| 209 | #123 | — | 6 | 4 | no | — |
| 210 | #123 | — | 6 | 8 | no | — |
| 211 | C22⋊Q8 | — | 2 | 4 | no | — |
| 212 | C22⋊Q8 | — | 3 | 8 | no | — |
| 213 | C22⋊Q8 | — | 6 | 4 | no | — |
| 214 | #121 | — | 3 | 8 | no | — |
| 215 | #121 | — | 6 | 4 | no | — |
| 216 | #121 | — | 6 | 4 | no | — |
| 217 | #120 | — | 6 | 4 | no | — |
| 218 | C4×Q8 | — | 2 | 4 | no | — |
| 219 | C4×Q8 | — | 3 | 8 | no | — |
| 220 | C4×Q8 | — | 6 | 4 | no | — |
| 221 | C4×D4 | — | 3 | 8 | no | — |
| 222 | C4×D4 | — | 6 | 8 | no | — |
| 223 | C4×D4 | — | 6 | 4 | no | — |
| 224 | C4×D4 | — | 6 | 8 | no | — |
| 225 | C4×D4 | — | 6 | 8 | no | — |
| 226 | C4×D4 | — | 6 | 4 | no | — |
| 227 | #117 | — | 6 | 4 | no | — |
| 228 | #117 | — | 6 | 8 | no | — |
| 229 | #117 | — | 6 | 4 | no | — |
| 230 | #117 | C22×D3 | 1 | 4 | yes | — |
| 231 | C2×C42 | — | 3 | 2 | no | — |
| 232 | C2×C42 | — | 3 | 1 | no | — |
| 233 | C2×C42 | — | 3 | 2 | no | — |
| 234 | C2×C42 | — | 3 | 2 | no | — |
| 235 | C2×C42 | — | 3 | 4 | no | — |
| 236 | C2×C42 | — | 6 | 4 | no | — |
| 237 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 238 | #107 | C22×D3 | 1 | 8 | yes | — |
| 239 | #106 | C22×D3 | 1 | 8 | yes | — |
| 240 | #103 | — | 3 | 16 | no | — |
| 241 | #102 | — | 3 | 16 | no | — |
| 242 | #97 | — | 3 | 4 | no | — |
| 243 | #97 | C22×D3 | 1 | 4 | yes | — |
| 244 | C4×C8 | — | 3 | 8 | no | — |
| 245 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×D3 | — | 2 | 2 | no | — |
| 247 | C22×D3 | — | 2 | 4 | no | — |
| 248 | C22×D3 | — | 4 | 2 | no | — |
| 249 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 250 | C3×Q8 | — | 4 | 8 | no | — |
| 251 | C2×C3×C4 | — | 2 | 8 | no | — |
| 252 | C2×C3×C4 | — | 4 | 2 | no | — |
| 253 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 254 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 256 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 257 | #67 | — | 4 | 8 | no | — |
| 258 | C2×Dic3 | — | 2 | 2 | no | — |
| 259 | C2×Dic3 | — | 2 | 4 | no | — |
| 260 | C2×Dic3 | — | 2 | 4 | no | — |
| 261 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 262 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 263 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 264 | D12 | — | 2 | 8 | no | — |
| 265 | D12 | — | 4 | 8 | no | — |
| 266 | D12 | — | 4 | 16 | no | — |
| 267 | C4×D3 | — | 2 | 4 | no | — |
| 268 | C4×D3 | — | 2 | 4 | no | — |
| 269 | C4×D3 | — | 2 | 8 | no | — |
| 270 | C4×D3 | — | 4 | 4 | no | — |
| 271 | C4×D3 | — | 4 | 8 | no | — |
| 272 | C4×D3 | — | 4 | 16 | no | — |
| 273 | Dic6 | — | 2 | 8 | no | — |
| 274 | C3×C8 | C2×#41 | 1 | 8 | yes | — |
| 275 | C3⋊C8 | — | 2 | 4 | no | — |
| 276 | C24 | — | 3 | 1 | no | — |
| 277 | #41 | — | 6 | 16 | no | — |
| 278 | #41 | — | 12 | 16 | no | — |
| 279 | C2×Q8 | — | 2 | 4 | no | — |
| 280 | C2×Q8 | — | 3 | 4 | no | — |
| 281 | C2×D4 | — | 3 | 4 | no | — |
| 282 | C2×D4 | — | 6 | 8 | no | — |
| 283 | C2×D4 | — | 6 | 4 | no | — |
| 284 | C2×D4 | — | 6 | 4 | no | — |
| 285 | C22×C4 | — | 3 | 2 | no | — |
| 286 | C22×C4 | — | 3 | 1 | no | — |
| 287 | C22×C4 | — | 3 | 4 | no | — |
| 288 | C22×C4 | — | 3 | 2 | no | — |
| 289 | C22×C4 | — | 3 | 2 | no | — |
| 290 | C22×C4 | — | 3 | 4 | no | — |
| 291 | C22×C4 | — | 6 | 8 | no | — |
| 292 | C22×C4 | — | 6 | 4 | no | — |
| 293 | C22×C4 | — | 6 | 4 | no | — |
| 294 | C22×C4 | — | 12 | 4 | no | — |
| 295 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 296 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 297 | Q16 | — | 6 | 8 | no | — |
| 298 | SD16 | — | 6 | 16 | no | — |
| 299 | D8 | — | 6 | 8 | no | — |
| 300 | M16 | — | 6 | 16 | no | — |
| 301 | C2×C8 | — | 3 | 4 | no | — |
| 302 | C2×C8 | — | 6 | 4 | no | — |
| 303 | C2×C8 | #239 | 1 | 8 | yes | complemented |
| 304 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 305 | C4⋊C4 | — | 2 | 4 | no | — |
| 306 | C4⋊C4 | — | 2 | 8 | no | — |
| 307 | C4⋊C4 | — | 6 | 8 | no | — |
| 308 | C4⋊C4 | — | 6 | 8 | no | — |
| 309 | C4⋊C4 | — | 6 | 4 | no | — |
| 310 | C4⋊C4 | C23×D3 | 1 | 8 | yes | — |
| 311 | C22⋊C4 | — | 2 | 4 | no | — |
| 312 | C22⋊C4 | — | 6 | 8 | no | — |
| 313 | C22⋊C4 | — | 6 | 8 | no | — |
| 314 | C22⋊C4 | — | 6 | 8 | no | — |
| 315 | C22⋊C4 | — | 6 | 8 | no | — |
| 316 | C42 | — | 2 | 4 | no | — |
| 317 | C42 | — | 3 | 4 | no | — |
| 318 | C42 | — | 3 | 4 | no | — |
| 319 | C42 | — | 3 | 1 | no | — |
| 320 | C42 | — | 3 | 1 | no | — |
| 321 | C42 | — | 3 | 2 | no | — |
| 322 | C42 | — | 6 | 8 | no | — |
| 323 | C42 | D3×D4 | 1 | 2 | yes | — |
| 324 | C42 | C23×D3 | 1 | 2 | yes | — |
| 325 | C22×C3 | — | 2 | 2 | no | — |
| 326 | C22×C3 | #532 | 1 | 2 | yes | — |
| 327 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 328 | C2×D3 | — | 2 | 2 | no | — |
| 329 | C2×D3 | — | 2 | 4 | no | — |
| 330 | C2×D3 | — | 4 | 4 | no | — |
| 331 | C2×D3 | — | 4 | 4 | no | — |
| 332 | C2×D3 | — | 4 | 8 | no | — |
| 333 | C3×C4 | — | 2 | 4 | no | — |
| 334 | C3×C4 | — | 4 | 8 | no | — |
| 335 | C3×C4 | #532 | 1 | 2 | yes | — |
| 336 | C3×C4 | C22×#41 | 1 | 2 | yes | — |
| 337 | Dic3 | — | 2 | 2 | no | — |
| 338 | Dic3 | — | 2 | 2 | no | — |
| 339 | Dic3 | — | 4 | 4 | no | — |
| 340 | Dic3 | #575 | 1 | 4 | yes | — |
| 341 | C23 | — | 3 | 2 | no | — |
| 342 | C23 | — | 6 | 2 | no | — |
| 343 | C23 | — | 6 | 4 | no | — |
| 344 | C23 | — | 12 | 2 | no | — |
| 345 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 346 | Q8 | — | 4 | 8 | no | — |
| 347 | Q8 | — | 6 | 8 | no | — |
| 348 | D4 | — | 6 | 8 | no | — |
| 349 | D4 | — | 12 | 8 | no | — |
| 350 | D4 | — | 12 | 16 | no | — |
| 351 | D4 | — | 12 | 8 | no | — |
| 352 | C2×C4 | — | 2 | 8 | no | — |
| 353 | C2×C4 | — | 3 | 2 | no | — |
| 354 | C2×C4 | — | 3 | 2 | no | — |
| 355 | C2×C4 | — | 3 | 2 | no | — |
| 356 | C2×C4 | — | 4 | 2 | no | — |
| 357 | C2×C4 | — | 6 | 8 | no | — |
| 358 | C2×C4 | — | 6 | 4 | no | — |
| 359 | C2×C4 | — | 6 | 2 | no | — |
| 360 | C2×C4 | — | 6 | 4 | no | — |
| 361 | C2×C4 | — | 6 | 4 | no | — |
| 362 | C2×C4 | — | 6 | 4 | no | — |
| 363 | C2×C4 | — | 12 | 4 | no | — |
| 364 | C2×C4 | — | 12 | 16 | no | — |
| 365 | C2×C4 | — | 12 | 8 | no | — |
| 366 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 367 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C2×#239 | 1 | 4 | yes | — |
| 369 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 370 | C8 | — | 6 | 4 | no | — |
| 371 | C8 | C2×#239 | 1 | 8 | yes | — |
| 372 | C2×C3 | — | 2 | 2 | no | — |
| 373 | C2×C3 | C2×#532 | 1 | 1 | yes | characteristic |
| 374 | C2×C3 | C2×#575 | 1 | 2 | yes | — |
| 375 | D3 | — | 4 | 2 | no | — |
| 376 | D3 | — | 8 | 4 | no | — |
| 377 | C22 | — | 2 | 2 | no | — |
| 378 | C22 | — | 6 | 4 | no | — |
| 379 | C22 | — | 6 | 2 | no | — |
| 380 | C22 | — | 12 | 4 | no | — |
| 381 | C22 | — | 12 | 8 | no | — |
| 382 | C22 | — | 12 | 4 | no | — |
| 383 | C22 | #5725 | 1 | 2 | yes | — |
| 384 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 385 | C4 | — | 2 | 4 | no | — |
| 386 | C4 | — | 3 | 4 | no | — |
| 387 | C4 | — | 4 | 8 | no | — |
| 388 | C4 | — | 6 | 2 | no | — |
| 389 | C4 | — | 6 | 2 | no | — |
| 390 | C4 | — | 12 | 4 | no | — |
| 391 | C4 | #5725 | 1 | 2 | yes | — |
| 392 | C4 | C22×#239 | 1 | 2 | yes | — |
| 393 | C3 | #60676 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 394 | C2 | — | 2 | 2 | no | — |
| 395 | C2 | — | 12 | 2 | no | — |
| 396 | C2 | — | 24 | 4 | no | — |
| 397 | C2 | C2×#5725 | 1 | 1 | yes | characteristic |
| 398 | C2 | D3×#575 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86257 | C2 | semidirect |
| 2. C3×#3162 | C2 | semidirect |
| 3. #83335 | C2 | semidirect |
| 4. #81959 | C2 | semidirect |
| 5. #81958 | C2 | semidirect |
| 6. #79181 | C2 | semidirect |
| 7. #79165 | C2 | semidirect |
| 8. #78499 | C2 | semidirect |
| 9. C2×#4707 | C2 | semidirect |
| 25. C3×#501 | C22 | semidirect |
| 29. #5089 | C22 | semidirect |
| 30. #5069 | C22 | semidirect |
| 31. #5067 | C22 | semidirect |
| 35. #4873 | C22 | semidirect |
| 36. #4872 | C22 | semidirect |
| 39. #4852 | C22 | semidirect |
| 40. #4715 | C22 | semidirect |
| 41. #4712 | C22 | semidirect |
| 46. #3162 | D3 | semidirect |
| 122. #501 | C2×D3 | semidirect |
| 161. C2×C3×C8 | #41 | semidirect |
| 303. C2×C8 | #239 | semidirect |
| 393. C3 | #60676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86257 | 2 |
| C3×#3162 | 2 |
| #83335 | 2 |
| #81959 | 2 |
| #81958 | 2 |
| #79181 | 2 |
| #79165 | 2 |
| #78499 | 2 |
| C2×#4707 | 2 |
| #60676 | 3 |